What is the solution for x*(dx)/(dt)=e^{3x}t ?

The solution for x*(dx)/(dt)=e^{3x}t is x=-(\W((9t^2+c_{1})/(2e)))/3-1/3

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x*(dx)/(dt)=e^{3x}t

x \cdot \frac{d x}{d t} = e^{3 x} t

x = - \frac{W ( \frac{9 t ^{2} + c _{1}}{2 e} )}{3} - \frac{1}{3}

Solution steps

x \cdot \frac{d x}{d t} = e^{3 x} t

Solve separable ODE:

x = - \frac{W ( \frac{9 t ^{2} + c _{1}}{2 e} )}{3} - \frac{1}{3}

x = - \frac{W ( \frac{9 t ^{2} + c _{1}}{2 e} )}{3} - \frac{1}{3}

What is the solution for x*(dx)/(dt)=e^{3x}t ?
The solution for x*(dx)/(dt)=e^{3x}t is x=-(\W((9t^2+c_{1})/(2e)))/3-1/3